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<p>This paper addresses the phenomenon of homoclinic chaos in a&#xa0;kinetic model with fast, intermediate, and slow variables. The model describes the dynamics of the heterogeneous catalytic reaction of interaction of hydrogen and oxygen on metallic catalyst. The subharmonic period-doubling cascade that is observed under a&#xa0;parameter variation in the system of three nonlinear ordinary differential equations leads to the generation of a&#xa0;global attractor. Using the Poincaré mapping and the second-iterate map, as well as their one-dimensional approximations, we prove the existence of a&#xa0;transversal homoclinic orbit to a&#xa0;saddle periodic Möbius orbit which generates the cascade of period-doubling bifurcations. The skeleton of the attractor consists of a&#xa0;family of unstable Möbius orbits of large periods. Numerical experiments show that a&#xa0;typical trajectory on the attractor under consideration is asymptotically chaotic.</p>

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Homoclinic Chaos in a Kinetic Model of Heterogeneous Catalytic Reaction

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Gennadii A. Chumakov,
  • Nataliya A. Chumakova

摘要

This paper addresses the phenomenon of homoclinic chaos in a kinetic model with fast, intermediate, and slow variables. The model describes the dynamics of the heterogeneous catalytic reaction of interaction of hydrogen and oxygen on metallic catalyst. The subharmonic period-doubling cascade that is observed under a parameter variation in the system of three nonlinear ordinary differential equations leads to the generation of a global attractor. Using the Poincaré mapping and the second-iterate map, as well as their one-dimensional approximations, we prove the existence of a transversal homoclinic orbit to a saddle periodic Möbius orbit which generates the cascade of period-doubling bifurcations. The skeleton of the attractor consists of a family of unstable Möbius orbits of large periods. Numerical experiments show that a typical trajectory on the attractor under consideration is asymptotically chaotic.